Find 2 numbers in an unsorted array equal to a given sum

Question

We need to find pair of numbers in an array whose sum is equal to a given value.

A = {6,4,5,7,9,1,2}

Sum = 10 Then the pairs are - {6,4} ,

Answer 1

If you assume that the value M to which the pairs are suppose to sum is constant and that the entries in the array are positive, then you can do this in one pass (O(n) time) using M/2 pointers (O(1) space) as follows. The pointers are labeled P1,P2,...,Pk where k=floor(M/2). Then do something like this

for (int i=0; i 0)
      print(Pj-1,i); // found a pair
      Pj = 0;
  } else
    if (Pj == 0)
      Pj = (i+1);    // found larger unpaired
    else if (Pj < 0)
      print(Pj-1,i); // found a pair
      Pj = 0;
  }
}

You can handle repeated entries (e.g. two 6's) by storing the indices as digits in base N, for example. For M/2, you can add the conditional

  if (j == M/2) {
    if (Pj == 0)
      Pj = i+1;      // found unpaired middle
    else
      print(Pj-1,i); // found a pair
      Pj = 0;
  } 

But now you have the problem of putting the pairs together.